Even when sealed Vodka does eventually go bad but it takes around 10 years before the sealed Vodka starts going bad and loses it's flavor.
If you want the Vodka to taste good then you should drink the Vodka before 10 years although after 10 years the sealed Vodka is still safe to drink but it won't be as good tasting.
Vodka doesn't get better with age unlike wine which tastes better the older it gets.
Vodka loses it's flavor after 10 years even when sealed and when you open a bottle of Vodka it will go bad much sooner.
A bottle of opened Vodka will usually go bad within 1 to 2 weeks even when refrigerated so make sure you drink the Vodka once opened within a week for the best taste.
So yes Vodka does go bad but it takes at least 10 years or more before it goes completely bad.